Question: ${3 \div \dfrac{3}{4} =}$
Answer: $3 \div \dfrac{3}{4}} ={\dfrac31} \div \dfrac{3}{4}} $ $~~~~~~~{\gray{\text{Rewrite 3 as }\dfrac31.}} $ $\phantom{3 \div \dfrac{2}{3}}} ={\dfrac31} \times \dfrac{4}{3}}$ $ ~~~~~~{\gray{\text{Multiply by reciprocal of }\dfrac34.}} $ $\phantom{8 \div \dfrac{2}{3}}} ={\dfrac{3\timesD4}{1\timesD3}} $ $~~~~~~~{\gray{\text{Multiply. }}} $ $\phantom{8 \div \dfrac{2}{3}}} ={\dfrac{12}{3}} $ $~~~~~~~{\gray{\text{Simplify. }}} $ $\phantom{8 \div \dfrac{2}{3}}} =4 $ ${3 \div \dfrac{3}{4} =4}$